Congruent Triangles  Why AAA doesn't work
Having all three corresponding angles equal is not enough to prove congruence
Try this
Drag any orange dot at P or R in the righthand triangle. It will change size while keeping all three angles congruent to the left triangle.
Notice that as you drag the points P or R, the triangle grows and shrinks so as it keeps all three
corresponding angles the same as the left triangle ABC. It is clear that the two triangles cannot be congruent because they can have
different sizes.
What does this mean?
It means that just because two triangles have congruent corresponding angles, it does not prove the triangles are congruent.
But they are similar
Triangles like this that are the same shape but different sizes are called similar triangles. For more on this see
Similar Triangles
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Other congruence topics
Congruent Triangles
Congruent Polygons
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